Math teaching needs to be more visual: New brain research says

By Courtesy of Stanford University

Researchers have dispeled the common belief that students should not use their fingers to learn mathematics

New evidence on how the brain functions when we think about mathematics could change the way mathematics is taught in K-12 and higher education classrooms. As described in the new paper released today, “SEEING AS UNDERSTANDING: The Importance of Visual Mathematics for our Brain and Learning,” supporting the use of visual mathematics and developing finger discrimination in students is vital for brain development and future mathematics success.

To download a copy of “SEEING AS UNDERSTANDING: The Importance of Visual Mathematics for our Brain and Learning,” visit www.youcubed.org/category/visual-math. The paper is authored by leading Stanford University mathematics researcher Dr. Jo Boaler and brain researcher Dr. Lang Chen.

“Our brains use visual pathways when we are learning math – our brains actually “see” a representation of fingers when we solve problems, whether or not we are actually using our fingers at the time, so training people on ways to perceive and represent their own fingers results in higher math achievement,” said co-author Dr. Jo Boaler, professor of mathematics education at Stanford Graduate School of Education and the co-founder of youcubed, a Stanford University center that provides research-based resources for teaching and learning mathematics. “Schools do not know about this important brain research and many schools even ban students from using fingers in classrooms. While Kumon learning centers tell parents they should not allow fingers to be used and it is a “no, no” for math learners, new research suggests that stopping students from counting on their fingers is akin to halting their mathematical development.”

According to the paper, educators and parents have to combat the issues around math instruction in today’s classrooms, including the focus on memorization, narrow presentations of math, the portrayal of finger counting as babyish and unhelpful, and the almost exclusive focus of schools on numerical and abstract thinking. Because the research shows that everyone uses visual pathways when they work on mathematics, parents and teachers need to develop the visual areas of children’s brains. They can do this by:

Using visuals, manipulatives and motion in mathematics teaching and parenting

Providing opportunities for students to use drawing, visualizing or working with models in mathematics

Teaching algebra visually through pattern study and generalization

Asking students, at regular intervals, how they see mathematical ideas

Asking students to represent mathematical ideas in a multitude of ways, such as through pictures, models, graphs, even doodles or cartoons

“Visual mathematics helps students at any level formulate ideas and develop understanding,” said Dr. Boaler. “In fact, the quality of six-year-olds’ perception and representation of fingers has been found to be a better predictor of future mathematics success than performance on tests of cognition.”

According to the authors, there is an urgent need to change the ways mathematics is offered to learners in order for them to function well in modern society as almost all new jobs require employees to make sense of “big data,” which includes seeing data patterns visually.

In addition to dispelling common beliefs about how children and adults learn math, the paper provides resources for parents and teachers to help students strengthen visual pathways in their brains and achieve at higher levels in mathematics. These resources can be found here <http://www.youcubed.org/category/visual-math/> . Last summer the youcubed team additionally provided five free visual mathematics lessons for grades 3-9 <http://www.youcubed.org/week-of-inspirational-math> that were downloaded one quarter of a million times and used in every state across the United States.

Dr. Jo Boaler is a professor of mathematics education at Stanford University and the co-founder of youcubed. She is also the author of the first MOOC on mathematics teaching and learning and the recipient of many awards, including the 2014 NCSM Equity Award. Dr. Boaler’s former roles have included being the Marie Curie Professor of Mathematics Education for Europe, a mathematics teacher in London comprehensive schools, and a researcher at King’s College, London University.

Dr. Lang Chen is a postdoctoral scholar in the Department of Psychiatry and Behavioral Science at Stanford University. His research focuses on the development of knowledge representations, currently in math and language, in the brain.